Anisotropies of charged particles accelerated in solar flares were studied by observing Doppler shifts of selected gamma-ray lines. The spectral shape was calculated of the 6.1-MeV line of O-16. If the accelerated particles are isotropic, the line remains centered at e sub 0 = 6129.4 keV, and its width (FWHM) is about 100 keV. For particle anisotropies that may be produced in solar flares, the line is shifted to lower energies by about 30 to 40 keV

Crannell, C. J.

Ramaty, R.

English

NASA Technical Reports Server

General Disclaimer 
One or more of the Following Statements may affect this Document 
 
 This document has been reproduced from the best copy furnished by the 
organizational source. It is being released in the interest of making available as 
much information as possible. 
 
 This document may contain data, which exceeds the sheet parameters. It was 
furnished in this condition by the organizational source and is the best copy 
available. 
 
 This document may contain tone-on-tone or color graphs, charts and/or pictures, 
which have been reproduced in black and white. 
 
 This document is paginated as submitted by the original source. 
 
 Portions of this document are not fully legible due to the historical nature of some 
of the material. However, it is the best reproduction available from the original 
submission. 
 
 
 
 
 
 
 
Produced by the NASA Center for Aerospace Information (CASI) 
https://ntrs.nasa.gov/search.jsp?R=19750016574 2020-03-22T22:01:29+00:00Z
i	 I
f
X-660-75-96
....,
NASAL .; X
. 
7e f?e
SOLAR GAMMA-RAY LINES AS PROBES
OF ACCELERATED PARTICLE
DIRECTIONALITIES IN FLARES
REUVEN RAMATY
CAROL JO CRANNELL
APRIL 1975
go
- GODDARD SPACE FLIGHT CENTER
GREENBELT, MARYLAND
(NASA-TM-X-70890)	 SOLAR GAMMA-: ,.AY LINhoi AS	 IN 5- 464b
PFOBFS OF ACCELERATED PAP.TICL.'.
DIFECTIONALITIES IN FLARES (NASA)	 13 p HC
$3.25	 CSCL 03B	 Unclas
63/92 21698
40
y
Solar Gamma-Ray Lines as Probes of
Accelerated Particle Directionalities in Flares
Reuven Ramaty and Carol Jo Crannell
NASA/Goddard Space Flight Center
Greenbelt, Maryland 20771
ABSTRACT
Anisotropies of charged particles accelerated in solar flares
can be studied by observing Doppler shifts of selected gamma-ray
lines. We have calculated the spectral shape of the 6.1-MeV line of
160. If the accelerated particles are isotropic, the line remains
centered at E o = 6124.4 keV, and its width (EHM) is about 100 keV.
However, for particle anisotropies that may be produced in solar
flares, the line is shifted to lower energies by about 30 to 40 keV.
- 2 -
I. INTRODUCTION
i
Emission lines in the gamma-ray band have been detected from the
large solar flares of 4 and 7 August 1972 (Chupp at al. 1973). The
observed lines,at 0.5, 2.2, 4.4 and 6.1 MeV, are due to positron
annihilation, neutron capture on hydrogen, and the deexcitation of
nuclear levels in 12C and 160, respectively (Lingenfelter and Ramaty
1967). The basic mechanism for the production of gamma-ray lines in
flares is interactions between primary accelerated particles and
atomic nuclei in the solar atmosphere (Ramaty at al. 1975).
The positrons and neutrons which result from these energetic
interactions are thermalized by the ambient medium before they
annihilate or get captured (Wang and Ramaty 1974, 1975). Therefore,
any directional anisotropies in the primary particles would be lost
before the gamma rays at 0.51 MeV and 2.2 MeV and produced. On the
ocher hand, the 12C and 160 nuclei, which emit the lines at 4.4 MeV
and 6.1 McV,are excited by protons of energies of several tens of
MeV which also impart kinetic energy to these nuclei. Because the
gamma rays are subsequently emitted in a time interval short compared
with the slowing-down time of the nuclei, any directional anisotropy in
the primary particles would cause a Doppler shift in the energy of
the lines.	 y1 present letter we calculate the Doppler shift of
the 6.1-MeV line 'or various angular distributions of the primary
i particles, and we show that observable Doppler shifts result from
particle anisotropies which might be present in solar flares.
h
- 3 -
II.	 Calculation of Line Profiles
The 6.1-MeV line in solar flares is produced by the reactions
160(p,p,)160*6,1 and 160(e,,(y,)160*6.1. Since both of these reactions
result in two bodies in the final state, the kinematics are straight-
forward, and the spectral shape of the deexcitation line is readily
determined from data on the differential cross sections of the
reactions. The 4.4-MeV line is produced by the corresponding reactions
in 12C, 
12C (p , p` ) 12C*4.4 and 12C	 12 *4.4(o ,p• ) C	 In addition, the
three-body reaction, 160(p,p V)12C*4.4, contributes to the 4.4"MeV
line. Because there are no data on the differential cross section
for this reaction, we limit our quantitative study in the present
letter to the 6.1-MeV line.
We use nonrelativistic kinematics. Because the total excitation
cross sections and the particle energy spectra decrease with increasing
energy, the energy range in which the majority of the contributing
interactions occur is limited to values less than about 100 MeV.
For such low kinetic energies, all the nuclear velocities are non-
velativistic.
Consider a projectile of mass m and velocity f3 (proton oro -
particle) interacting with an oxygen nucleus of mass M. Let the
excited nucleus emerge from the reaction with a velocity p s* and
directional cosine us * with respect to the projectile's velocity
vector in the center of mass frame. (The speed of light is taken to
be unity.) Because there are only 2 bodies in the final sta-e, Os*
is uniquely determined by p:
f	 _
- 4 -
I
	
ge* 	 Be  - 2(AE)m/[ M(m + M)].	 (1)
Here 9c = om/(m + M) is the velocity of the center of mass, and
AE a 6130.66 ± .18 keV (Ajzenberg-Se love 1971) is the energy of the
3 level in 160. This level decays to the ground state by an electric
octopole transition and has a lifetime of about 10 -11a (Hellwege and
Hel'lwege 1961). The velocity and directional cosine of the oxygen nucleus
in the frame of the Sun are
$a 2 = 
Be t + Bs*2 + 20c RB µs* ,	 ( 2)
and
As = (Be + 0 s*As* )/Bs . 	(3)
We denote by gry the cosine of the angle between the 6.1-MeV gamma ray
and the velocity vector of the oxygen nucleus in the rest frame of this
nucleus. in the frame of the Sun, this directional cosine is
Fry = (6s + u'y)/(1 + 0 sµ.').	 (4)
Taking into account the Doppler shift, the energy of the gamma ray is
given by
E 
	 = Eo (1 + (3 sµy ),	 (5)
where E  is its energy in the rest frame of the emitting nucleus. Because
the oxygen nucleus recoils when it emits a photon, E  is slightly less
than AE,
E o = AE - (AE) 2/(2M) = 6129.4 keV	 (6)
Finally, the cosine of the angle between the gamma ray and the velocity
vector of the projectile is
u = Jaswy + (1-µs 2 ) 1/2 ( 1 -uy 2 ) 1/2cos (0s- 07 ),	 (7)
r
- 5 -
where 0. - Oy is the difference between the azimuths of the projectile
and gamma ray in a plane perpendicular to the velocity of the oxygen.
We used a Monte-Carlo simulation to calculate the energy distribution
of the gamma rays. The directional cosines alai and u7 ' are assumed to
s^
be uniformly distributed random numbers in the range - 1 to 1. For us
this assumption is consistent with data on the differential cross section
for the reactions 16 0(p p')160Or6.1 and 
160 
&,V 1 ) 16 0 *6.1  (Kobayashi 1960,
Bergman and Hobbie 1971). For qty' the above assumption simply means
that the gamma rays are emitted isotropically in the rest frame of the
oxygen nucleus. A random number is also assigned to the projectile
velocity, 5. The distribution of thin. number is determined by the energy
spectrum of the primary particles and the energy dependence of the total
cross section. We have used the 3ata compiled by Bamaty et al. ( 1975),
and we assumed that the differential number spectrum of the primary
particles is a power law with spectral index 2.
If the distribution of projectile velocities is isotropic, all the
gamma rays generated by the simulation contribute to the spectrum, regard-
less of the value of g, the cosine of the angle between the projectile
and the gamma ray. The results for this case are shown by the solid
curves in Figures la and lb, for proton and o,-particle induced reactions,
respectively. As can be seen, the resultant spectra are almost symmetric.
The small blue shift, however, is real. It is caused by the finite velo-
cities of the emitting nuclei which transform the isotropic rest—frame
radiation patterns into patterns peaked in the direction of motion. The
blue shift is due to the fact that radiation seen by any observer comes,
on the average, more from nuclei having velocity components toward the
observer than away from him.	 19
- 6 -
We consider now gamma-ray spectra resulting from projectiles with
anisotropic velocity distributions. The dashed curves in Figures is
and lb show the gamma-ray spectrum produced by projectiles whose velocity
vectors are uniformly distributed in hemisphere away from the observer,
and the dashed-dotted curves represent a case in which the projectiles
are directed away from the observer in a cone of half angle 60 °. In
the Monte-Carlo simulation the angle µ is obtained from equation (5)
with 0e - Ott being a uniformly distributed random number between 0 and
2rR; only those events which satisfy the conditions -l5µ50 or -15µ5-0.5
contribute to the respective spectra.
Both anisotropic angular distributions cause large red shifts. For
proton-induced reactions, the shift in the peak of the spectrum ranges
from about 25 keV to 35 keV. For ir-particle induced reactions the shift
ranges from about 40 keV to 60 keV. The relative contribution of the
protons and alpha particles depends on the spectral indices of the particle-
energy distributions (Ramaty at al. 1975). For a spectral index of 2,
as was assumed in the present calculations, 20% of the gamma rays result
from a-particle-induced reactiuns. The shift of the composite gamma-ray
spectrum then ranges from approximately 30 to 40 ke y'. If the angular
distribution of the projectiles were more sharply peaked forwerd, rather
than being uniform within the prescribed boundaries, the shift of the
gamma-ray spectrum would be even larger.
The excited state 160*6.1 can also be produced by accelerated oxygen
x,
1 nuclei interacting with ambient hydrogen and helium. Since the Doppler
widths of the resultant line are about 1 MeV, this radiation cannot be
i
- 7 -
distinguished from the continuum and does not contribute to line emission.
III. Discussion and Conclusions
Redshifts of the order of several tens of keV are large compared with
the energy resolution (w 3 keV) of presently available detectors (Metzger
1973), and hence su-.h detectors should be able to measure these redshifts.
The detection of redshifts in solar gamma-ray lines would support flare
models in which particle acceleration occe.:6 at coronal heights and the
nuclear interactions are produced by particle fluxes directed downward
towards the Saran (e.g. Sturrock 1973). Since the magnitude of the redshift
depends on the angle between the particle beam and direction of observation,
the location of the flare on the Sun will also have an effect on the observed
redshifts. Because of their limited energy resolution, the present
measurements of Chupp at al. (1973) cannot provide information on the
spectral shape or precise energy of the 4.4-and 6.1-MeV lines.
The determination of tha spectral shapes of nuclear deexcitation
lines from solar flares will be complicated by background radiations
and confusion between lines. For example, the 6.1-MeV line of 160
could be confused with the 6.3-MeV line of 15N. The latter is produced
by the reaction 0(p,2p) 15N	 with comparable intensity to that of
the 6.1-MeV line (Ramaty et a1. 1975). However, because the separation
between these two lines, 198 keV, is larger than their broadening, we
expect that they will be separable with detectors having high energy
resolution.
As discussed in the Introduction, the energies of the 2.2-MeV and
0.51-MeV lines are not affected by the anisotropy of the primary particles.
- 8 -
The 2.2-MeV line, in particular, has a very narrow width of only 100 eV
and its energy is accurately known to be 2223.0 keV independent of any
solar parameter (Ramaty et al. 1975). Therefore, this line can be used
as a calibration point of the flare spectrum, independent of charged
particle anisotropies. For the 4.4-MeV line of 12C we expect comparable
redshifts and spectral broadening as for the 6.1-MeV line.
In summary, high-resolution observations of the spectral-shape and
mean energy of selected y-ray lines would provide a new measure of the
role of accelerated particles in the dynamics of solar flares.
Acknowledgements
We would like to acknowledge discussions of this problem with
T. Bai, E. Chupp, T. Cline, H. Crannell, L. Fisk, C. Ryter, B. Teegarden,
J. Trombka and H. Wang.
-9..
REFERENCES
Ajzenberg-Selove, F. 1971, Nuclear Physics A, 166, 1.
Bergman, C. and Hobbie, R. K. 1971, Physical Review C, 3, 1729.
Chupp, E. L., Forrest, D. J., Higbie, P. R., Suri, A. N., Tsai, C., and
Dunphy, P. P. 1973, Nature, 241, 333.
Hellwege, A. M. and Hellwege, K. H. 1971, Energy levels of Nuclei:
A - 5 to A - 257,(Springer-Verlag, Berlin).
Kobayashi., S. 1960, J. Phys. Sec. Japan, 15, 1164.
Lingenfelter, R. E. and Ramaty, R. 1967, High Energy Nuclear Reactions in
Astrophysics, edited by B. S. P. Shen (W. A. Benjamin, New York),
P. 99.
Metzger, A. 1973, Gamma Ray Astrophysics, edited by F. W. Stecker and
J. 1. Trombka, NASA SP-339, (National Aeronautics and Space
Administration, Washington, D. C. ), p. 97.
Ramaty, R., Kozlovsky, B. and Lingenfelter, R. E. 1975, Space Science
Reviews, in press.
Sturrock, P. A. 1973, High Energy Phenomena on the Sun, edited by
R. Ramaty and R. G. Stone, NASA SP-342 (National Aeronautics and
Space Administration, Washington, D. C.), p. 3.
Wang, H. T. and Ramaty, R. 1974, Solar Physics 36, 129.
Wang, H. T. and Ramaty, R. 1975, to be published.
- 10 -
FIGURE CAPTION
Energy spectra of gamma rays from the reactions (a) 16O(p'p,)160*6.1
and (b) 160(a'al)160*6.1 The solid lines were obtained from an
isotropic distribution of protons and alpha particles and are normalized
such that the integral of O(Ey) is unity. The dashed and dashed-dotted
curves are obtained from the same distribution, having the same normal-
ization e? the isotropic case, with the additional restriction that µ,
the cosine of the angle between the direction of observation and
proton or a-particle velocities, lies within the indicated ranges.
Y
0.01
160( P, Pl)1s0*s.1
	.008	 (a)
.006
.004
.002
Y	 ^.
cn	 0
F--
m 0.01
a	 0(a,a') 0E - 6129.4 keVo'
	
w .008	
-I5µ<_ IV
N' -
	
.006
	
- — - I5µ5 -0.5
(b)
	.004	 ^^,-
	
.002	 ^`•	 `^
0
-120 -80 -40 0
	 40 80 120
(EY -Ea) (keV)
L
e


Solar gamma-ray lines as probes of accelerated particle directionalities in flares

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server